As nouns the difference between engineer and supervisor is that engineer is a person who is qualified or professionally engaged in any branch of engineering while supervisor is (management) a person with the official task of overseeing the work of a person or group.
As a verb engineer is to design, construct or manage something as an engineer.
As nouns the difference between design and engineer is that design is a plan (with more or less detail) for the structure and functions of an artifact, building or system while engineer is a person who is qualified or professionally engaged in any branch of engineering. As verbs the difference between design and engineer is that design is (obsolete) to assign, appoint (something (to) someone); to designate while engineer is to design, construct or manage something as an engineer.
As nouns the difference between engineer and specialist is that engineer is a person who is qualified or professionally engaged in any branch of engineering while specialist is someone who is an expert in, or devoted to, some specific branch of study or research. As a verb engineer is to design, construct or manage something as an engineer. As an adjective specialist is (british) specialised.